Over 38 percent of children with Facebook accounts are 12-years-old and under. Even more worryingly, 4 percent of children on Facebook are reported to be 6-years-old or younger, which translates to some 800,000 kindergarteners on Facebook.

The results come from a survey of 1,000 parents of children under 18-years-old who use Facebook, conducted by MinorMonitor. The company provides a free, web-based parental tool that gives parents a quick view into their child's Facebook use, including potential dangerous activities such as the friending of online predators, cyberbullying, violence, drug and alcohol use, as well as sexual references.

74 percent of parents are concerned about their children's safety on Facebook, with 56 percent worrying about sexual predators, a far larger percentage than 11 other "worry" categories. 41 percent of parents said they were concerned about cyberbullying through Facebook use, while 30 percent of parents believed their child already experienced cyberbullying.

Over 50 percent of parents currently monitor their children's Facebook activities by logging into their child's account, with or without their child's permission. 24 percent of parents feel they are monitoring their child on Facebook by friending them, an extremely ineffective way to get to the heart of real concerning activities. 17 percent admitted they just aren't monitoring their children at all.

"Some parents believe that 'friending' their child on Facebook is adequate to ensure safety," Mike Betron, VP and General Manager of MinorMonitor, said in a statement. "This simply provides a false sense of security as children are still able to engage in private conversations and post questionable material without their parents seeing this as a friend."

You can see more of the results in the following infographic:

MinorMonitor offered the following tips for parents:

Know children's passwords and other login information, and teach your children not to share their passwords or personal information.

Keep Facebook profiles set to private, and know Facebook's other built-in safety features.

Teach children about friending and that all requests from strangers should be declined.

Remind children that information posted online is public.

The Children's Online Privacy Protection Act (COPPA) mandates that websites that collect information about users aren't allowed to sign on anyone under the age of 13. As a result, Facebook's Statement of Rights and Responsibilities require users of the social network to be at least 13 years old (and even older, in some jurisdictions).